1 Inventory Control Chapter 17. 2 Inventory System Inventory is the stock of any item or resource used in an organization and can include: raw materials,

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Inventory Control

Chapter 17

2

Inventory System Inventory is the stock of any item or

resource used in an organization and can include: raw materials, finished products, component parts, supplies, and work-in-process

An inventory system is the set of policies and controls that monitor levels of inventory and determines what levels should be maintained, when stock should be replenished, and how large orders should be

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Purposes of Inventory

1. To maintain independence of operations

2. To meet variation in product demand

3. To allow flexibility in production scheduling

4. To provide a safeguard for variation in raw material delivery time

5. To take advantage of economic purchase-order size

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Inventory Costs

Holding (or carrying) costs– Costs for storage, handling,

insurance, etc Setup (or production change) costs

– Costs for arranging specific equipment setups, etc

Ordering costs– Costs of someone placing an order,

etc

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E(1)

Independent vs. Dependent Demand

Independent Demand (Demand for the final end-product or demand not related to other items)

Dependent Demand

(Derived demand items for

component parts,

subassemblies, raw materials,

etc)

Finishedproduct

Component parts

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Inventory Systems Single-Period Inventory Model

– One time purchasing decision (Example: vendor selling t-shirts at a football game)

– Seeks to balance the costs of inventory overstock and under stock

Multi-Period Inventory Models– Fixed-Order Quantity Models

Event triggered (Example: running out of stock)

– Fixed-Time Period Models Time triggered (Example: Monthly sales call

by sales representative)

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Multi-Period Models:Fixed-Order Quantity Model Model Assumptions (Part 1)

Demand for the product is constant and uniform throughout the period

Lead time (time from ordering to receipt) is constant

Price per unit of product is constant

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Multi-Period Models:Fixed-Order Quantity Model Model

Assumptions (Part 2)

Inventory holding cost is based on average inventory

Ordering or setup costs are constant

All demands for the product will be satisfied (No back orders are allowed)

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Basic Fixed-Order Quantity Model and Reorder Point Behavior

R = Reorder pointQ = Economic order quantityL = Lead time

L L

Q QQ

R

Time

Numberof unitson hand

1. You receive an order quantity Q.

2. Your start using them up over time. 3. When you reach down to

a level of inventory of R, you place your next Q sized order.

4. The cycle then repeats.

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Cost Minimization Goal

Ordering Costs

HoldingCosts

Order Quantity (Q)

COST

Annual Cost ofItems (DC)

Total Cost

QOPT

By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs

By adding the item, holding, and ordering costs together, we determine the total cost curve, which in turn is used to find the Qopt inventory order point that minimizes total costs

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Basic Fixed-Order Quantity (EOQ) Model Formula

H 2

Q + S

Q

D = TC H

2

Q + S

Q

D = TC

Total Annual =Cost

AnnualOrdering

Cost

AnnualHolding

Cost+

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

TC=Total annual costD =DemandC =Cost per unitQ =Order quantityS =Cost of placing an order or setup costR =Reorder pointL =Lead timeH=Annual holding and storage cost per unit of inventory

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Deriving the EOQUsing calculus, we take the first derivative of the

total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Using calculus, we take the first derivative of the total cost function with respect to Q, and set the derivative (slope) equal to zero, solving for the optimized (cost minimized) value of Qopt

Q = 2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPTQ =

2DS

H =

2(Annual D em and)(Order or Setup Cost)

Annual Holding CostOPT

Reorder point, R = d L_

Reorder point, R = d L_

d = average daily demand (constant)

L = Lead time (constant)

_

We also need a reorder point to tell us when to place an order

We also need a reorder point to tell us when to place an order

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EOQ Example (1) Problem Data

Annual Demand = 1,000 unitsDays per year considered in average

daily demand = 365Cost to place an order = $10Holding cost per unit per year = $2.50Lead time = 7 daysCost per unit = $15

Given the information below, what are the EOQ and reorder point?

Given the information below, what are the EOQ and reorder point?

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EOQ Example (1) Solution

Q = 2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 unitsQ =

2DS

H =

2(1,000 )(10)

2.50 = 89.443 units or OPT 90 units

d = 1,000 units / year

365 days / year = 2.74 units / dayd =

1,000 units / year

365 days / year = 2.74 units / day

Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units Reorder point, R = d L = 2.74units / day (7days) = 19.18 or _

20 units

In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.

In summary, you place an optimal order of 90 units. In the course of using the units to meet demand, when you only have 20 units left, place the next order of 90 units.

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EOQ Example (2) Problem Data

Annual Demand = 10,000 unitsDays per year considered in average daily demand = 365Cost to place an order = $10Holding cost per unit per year = 10% of cost per unitLead time = 10 daysCost per unit = $15

Determine the economic order quantity and the reorder point given the following…

Determine the economic order quantity and the reorder point given the following…

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EOQ Example (2) Solution

Q =2DS

H=

2(10,000 )(10)

1.50= 365.148 units, or OPT 366 unitsQ =

2DS

H=

2(10,000 )(10)

1.50= 365.148 units, or OPT 366 units

d =10,000 units / year

365 days / year= 27.397 units / dayd =

10,000 units / year

365 days / year= 27.397 units / day

R = d L = 27.397 units / day (10 days) = 273.97 or _

274 unitsR = d L = 27.397 units / day (10 days) = 273.97 or _

274 units

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

Place an order for 366 units. When in the course of using the inventory you are left with only 274 units, place the next order of 366 units.

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Fixed-Quantity Model with random Lead time Demand

Answer how much & when to order Allow demand to vary

– Follows normal distribution– Other EOQ assumptions apply

Consider service level & safety stock– Service level = 1 - Probability of stockout– Higher service level means more safety stock

More safety stock means higher ROP

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Probabilistic ROPWhen to Order?

Reorder Point

(ROP)

Optimal Order

Quantity X

Safety Stock (SS)

Time

Inventory Level

Lead Time

SSROP

Service Level P(Stockout)

Place order

Receive order

Frequency

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ROP = 350 + 1.65*10 = 366.5 or 367 units

Reorder Point Example

A company experiences mean demand during lead time of 350 and std. dev. of LTD of 10

ROP = Average demand during lead time + Safety stock

SS = z * stdev of lead time demand (LTD normally distributed)

For 95% service level, z = 1.65

ROP = Average demand during lead time + Safety stock

SS = z * stdev of lead time demand (LTD normally distributed)

For 95% service level, z = 1.65

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Answers how much to order Orders placed at fixed intervals

– Inventory brought up to target amount– Amount ordered varies

No continuous inventory count– Possibility of stockout between intervals

Useful when vendors visit routinely– Example: P&G representative calls every 2

weeks

Fixed-Time Period Model

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Inventory Level in a Fixed Period System

Various amounts (Qi) are ordered at regular time intervals (p) based on the quantity necessary to bring inventory up to

target maximum

pp pp pp

QQ11 QQ22

QQ33

QQ44

Target maximum

TimeTime

On-

Hand

Inve

ntor

yO

n-Ha

nd In

vent

ory